The S&P 500 was up 1.3%, the Dow Jones Industrial Average added 1.6%, or 281 points, and the Nasdaq gained 1.2%. The S&P 500 remains in correction territory, though, having fallen 12% from its 52-week high.

Stocks have suffered from unpredictable and steep moves since the beginning of the year as worries over global growth and a relentless slide in commodities kept equities under pressure. Despite Tuesday's rally, we might not have reached the end to this selloff just yet.

"There's still ... concerns about growth and where we're headed," Robert Pavlik, chief market strategist at Boston Private Wealth, told CNBC. "People are concerned they don't know where energy prices are heading, they don't know what the [Federal Reserve] is going to be saying."

Crude oil endured more big swings as prices rebounded on Tuesday after a massive selloff a day earlier. West Texas Intermediate crude oil gained 3.7% to close at $31.45 a barrel. Prices have been under pressure on signs major oil producers such as Saudi Arabia will ramp up production despite massive global oversupply.